I just redeemed a few games from Amazon Prime Gaming today and to my surprise was greeted while redeeming the code on the GOG website by three different 3rd-Party company ads during that process, congratulating me for my 'free money' ("You earned a 10$ gift card ... do you want to accept, click yes/no".

These three companies - offering their services via a contract with GOG.com - are making their money from selling user data, once an innocent soul accepted this offer. The users are then bound to share their data (collected from GOG ... AND all the other website partners on the Internet!) and be subject to data profiling, tracking and marketing. The (one time) 'free gift-card' or 'discount' offers are the way to lure people in.

While this is by no means illegal business practice, even inside the EU (everyone can click on 'skip' ... for now), this is a surprisingly shady 'upgrade' to the GOG Store user experience?

Redeeming a free code from an Amazon Prime (paid) subscription partnered with GOG is one thing. Being subject to targeted marketing and being lured into contracts by unrelated, aggressive 3rd party companies is quite another level of shady, altogether?

I would hope that CD Project - wholly subsidiary owner of GOG sp. z o.o. - will stop this practice and stick to making and selling and distributing games, instead.

Your reputation will suffer and reputation is the currency which allows you to have customers?

If the ad said "Powered by Rokt" in the corner, then no, it's not new:
https://www.gog.com/forum/general/ads_when_redeeming_gaming_amazon_code/post21

You should only get those if you explicitly agreed to the relevant cookies when the prompt popped up. Supposedly it's possible to retract your consent by clicking "Cookie Declaration" in the footer at the bottom, but I can't get that link to work. If you have the same issue, simply clearing browser cookies from GOG should do the trick. Not agreeing to the cookies should be functionally the same as declining.